Problem: When the set of natural numbers is listed in ascending order, what is the smallest prime number that occurs after a sequence of five consecutive positive integers all of which are nonprime?
Solution: Consider the differences between consecutive prime numbers and look for the first difference of 6 or greater.  The first several prime numbers are \[
2,3,5,7,11,13,17,19,23,29,31, 37,\ldots,
\] and the differences between consecutive terms of this sequence are  \[
1,2,2,4,2,4,2,4,6,2,\ldots.
\] The first appearance of a difference of 6 or greater occurs between 23 and $\boxed{29}$.